Home Affairs Minister Peter Dutton has threatened to turn the tables on the Labor opposition if it keeps pursuing him over the au pair scandal, saying he "kept a list" of MPs who asked him for help on immigration cases and he is "gathering information" to expose Labor's hypocrisy.

Meanwhile, Labor and the Greens have announced they will increase the pressure on Mr Dutton with a no confidence motion when Parliament returns next week, which will test the government's control of the House of Representatives.

They will also use a Senate inquiry this week to probe the au pair controversy. Mr Dutton on Monday insisted he had "nothing at all to hide" and challenged Labor to interrogate him in the chamber.

"Labor can ask me 10 questions every day when we go back if that’s what they want to do, but they’ll get a whack back," he said.

Home Affairs Minister Peter Dutton has accused the Labor Party of "hypocrisy".Credit:Alex Ellinghausen

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"I’ve got a series of cases that have been put to me by Labor members - and I’ve kept a very good list, actually, of MPs who have come to me with quirky cases.

"I will be happy to go into some matters in question time, potentially. I’m gathering some of that information at the moment - because I’ve been quite gobsmacked by the hypocrisy from some of those within the Greens and Labor."

There is no suggestion Mr Dutton went beyond his power as the minister to overturn visa decisions. But his critics say he has questions to answer about whether the interventions amounted to favours for mates.

Greens MP Adam Bandt said he would move a motion of no confidence in Mr Dutton on the basis he misled Parliament in March when he denied any personal connection to the intended employers' of the au pairs.

Labor will support the ploy. With former prime minister Malcolm Turnbull gone, and the Nationals' Kevin Hogan on the crossbench, the government's numbers in the lower house are less certain.

The motion will still fail unless some Coalition MPs abstain, miss the vote or support the motion. Even if it succeeds, Mr Dutton's position in cabinet would still be at the discretion of Prime Minister Scott Morrison, who so far backed his minister.

Mr Morrison said it was a "furphy" that the minister had misled Parliament when he denied any personal connection to the intended employers of the au pairs.

Mr Dutton told reporters on Monday that he was "a person of high integrity". He also suggested he was the victim of mud-slinging by "someone disaffected within Australian Border Force".

In an apparent response, former ABF commissioner Roman Quaedvlieg used his Twitter account to make "two interesting points about self-proclamations of integrity".

"They aren’t particularly valuable nor convincing, other than to the proclaimer," he wrote.

"They never occur outside of a crisis which invokes them. Who ever heard a spontaneous one?"

Mr Quaedvlieg declined to comment when asked.

Mr Dutton also raised questions about shadow treasurer and former immigration minister Chris Bowen. He said Mr Bowen - who holds a multicultural seat in Sydney's west - had written to him "hundreds of times" seeking his intervention in visa cases.

"Has he got a personal connection to any of those people?" Mr Dutton asked. "You would need to ask him that."

Mr Bowen told Fairfax Media: "Of course I have made representations on behalf of my constituents. That is my job."

"I can confirm that at no stage have I made any representations on behalf of au pairs at airports who are pretty clearly in breach of the rules. And neither did I, during my three years as immigration minister, approve any."